To determine which scenario models the equation \( 2x = 125 - 12x \), let's analyze both options:
-
First Scenario: The Garcia family is driving to a vacation spot that is 125 miles away, and after two hours of driving, they are half an hour short of reaching it. The key variables here are the distance driven and the time taken. If we consider their rate of speed as \( x \) miles per hour, then after two hours, they have driven \( 2x \) miles. The family is then still half an hour away from their destination, meaning they can cover that remaining distance in additional time. To calculate the equation, we can determine that they should be driving the remaining distance of \( 125 - 2x \) in the half hour they have left. Since they can cover \( 0.5x \) miles in half an hour, we can set up the equation: \[ 2x + 0.5x = 125 \] Simplifying gives: \[ 2.5x = 125 \] However, this does not directly match the equation \( 2x = 125 - 12x \).
-
Second Scenario: A construction company has three barrels of cement, where two full barrels together weigh 125 pounds more than the third barrel, which is half full. If we let \( x \) represent the weight of the third barrel when full, then the weight of the two full barrels is \( 2x \), and the weight of the half-full barrel would then be \( 0.5x \). The relationship can be set up as: \[ 2x = 0.5x + 125 \] When rearranging this equation, we have: \[ 2x - 0.5x = 125 \] Which simplifies to: \[ 1.5x = 125 \] When multiplied throughout by 2, it converges to a similar structure but backward, so while it does align somewhat, it’s less clear.
To visibly manipulate \( 2x = 125 - 12x \):
- Rearranging gives \( 2x + 12x = 125 \) ⇒ \( 14x = 125 \).
In summary, scenario 1 is more aligned with an equation focusing on distance traveled vs remaining distance, compared to scenario 2, which more directly results in a straightforward algebraic relationship without additional complexity varying with time and space traveled.
Final Answer: Scenario 1 closely models the equation \( 2x = 125 - 12x \).